Confidence Intervals for a Binomial Parameter after Observing No Successes

Abstract

The easily computed, one-sided confidence interval for the binomial parameter provides the basis for an interesting classroom example of scientific thinking and its relationship to confidence intervals. The upper limit can be represented as the sample proportion from a number of “successes” in a future experiment of the same sample size. The upper limit reported by most people corresponds closely to that producing a 95 percent classical confidence interval and has a Bayesian interpretation.

Key Words:

• Binomial confidence interval
• Subjective beliefs
• Bayesian inference
• The .05 level